A Probabilistic Functional Approach to Analyzing Individual Evaluation of Compiled Nutrition Information

Paul Prabhaker, SUNY at Buffalo
Paul Sauer, SUNY at Buffalo
ABSTRACT - This research examines variation in consumer use of nutrient cues for 40 brands of dry cereal in forming a summary nutritional evaluation of each brand. Brunswik's lens model technique is used to analyze probabilistic linear and non-linear cue utilization on a subject by subject basis. Results reveal considerable between subject variation in cue use as well as inverse use of negative nutrient cues. The extent of between subject variation challenges previous assumptions of homogeneity of cue usage in cross sectional studies.
[ to cite ]:
Paul Prabhaker and Paul Sauer (1988) ,"A Probabilistic Functional Approach to Analyzing Individual Evaluation of Compiled Nutrition Information", in NA - Advances in Consumer Research Volume 15, eds. Micheal J. Houston, Provo, UT : Association for Consumer Research, Pages: 83-88.

Advances in Consumer Research Volume 15, 1988      Pages 83-88


Paul Prabhaker, SUNY at Buffalo

Paul Sauer, SUNY at Buffalo


This research examines variation in consumer use of nutrient cues for 40 brands of dry cereal in forming a summary nutritional evaluation of each brand. Brunswik's lens model technique is used to analyze probabilistic linear and non-linear cue utilization on a subject by subject basis. Results reveal considerable between subject variation in cue use as well as inverse use of negative nutrient cues. The extent of between subject variation challenges previous assumptions of homogeneity of cue usage in cross sectional studies.


Every person's concern with physical health and wellbeing involves consideration of their diet composition, based upon evaluation of the nutritional content of the foods which they consume. Such evaluation is facilitated by the availability of nutritional information which reveals the nutrient content of various food groups. This study examines the variation in the use of one type of nutritional data for one specific type of food, breakfast cereals.

Breakfast cereals were chosen because there is a great amount of variation across brands in nutritional content and a large variety of brands are available. Nutritional value was found to be one of four attributes of cereal most frequently mentioned by subjects in choosing which brand to purchase (Gatignon, 1984). Nutrition has been shown to effect purchase change as well as have no effect on purchase depending upon the type of nutritional information available. (see Russo, et al., 1986 for an excellent review)

The following section briefly discusses the background for consumer's evaluation of nutritional information. A probabilistic functional approach is used to structure the analysis of variation in consumer use of nutrient cues. The purpose of this study is to compare the variation across individuals in the use of nutrition information with that of an "expert" source.


Food processors and packagers are required by law to print the ingredients of a product on the package. This information includes the food (e.g. beef, pork), coloring, (e.g. red dye No. 7), chemical, (e.g., sodium nitrate, preservatives), and additive, (e.g., salt, vinegar) content, but only about half of all packaged products include the nutrient content (e.g., proteins, carbohydrates) (Consumer Reports, March 1986). One product which does include nutrient information on the label is dry breakfast cereals. Consumer concern with the nutrient content of cereals makes this type of information promotionally appealing.

The costs of collecting, computing, and comprehending sufficient nutrition information by examining each cereal box on a supermarket shelf is prohibitively high to most consumers. Few consumers actually acquire such information (Jacoby, Chestnut and Silberman, 1977). To reduce these costs to an acceptable level, Russo, et.al. (1986) provided consumers with an information display board placed near cereal shelves in supermarkets. Four formats were used: matrix; summary; intermediate; and, complete. While useful in their experimental setting, such information formats are usually not available to consumers in supermarket displays. What is available is similarly formatted information in generally circulated publications.

For purposes of our study, we chose to use the information available in a recent issue of Consumer Reports (October 1986). Consumer Reports product evaluations have been influential in significantly altering sales and have been the subject of legislation concerning advertising use of its product evaluation techniques (Consumer Reports, November 1986). The information is typically provided in the complete format. That is, cereal nutrient content by brand is provided in a matrix format which includes a summary rating of overall nutritional value for each brand calculated from the nutrient data in the matrix.

The inclusion of a summary measure in the complete format provides an interval scaled basis for the rank ordering of brands. It raises the question as to how consumers actually use such information in brand comparisons and decisions. To simply accept the summary measure as a basis of personal evaluation implies that the consumer agrees with the weighting and combinatorial mathematics which Consumer Reports employs in deriving the summary measure, regardless of each consumer's own needs, preferences, or opinions.

In a recent study, fifty-four percent of consumers using a German equivalent of Consumer Reports were found to rely on summary measures in the purchase of nondurables, while only eleven percent used the individual attribute (e.g. nutrient) ratings in the adjoining matrix (Silberer, 1985). Such use of summary measures subjugates consumers to the combinatorial mathematics, linear or configural, utilized by the publication in creating the overall summary measures. This willingness on the part of consumers to rely on summary measures likely reflects a cost versus benefit analysis of information acquisition rather than a true indication of each consumers importance weight with respect to each attribute. It also may reflect the credibility which the publication has earned in the mind of the consumer.

The nutrient information provided by Consumer Reports includes five nutrients from which the summary rating is computed for each brand. Vitamin and mineral content is not included. Russo, et.al. (1986) found that positive nutrient information such as vitamins and minerals had no effect on brand purchases, but that "negative" nutrient (sugar) information did affect brand purchase patterns. The Consumer Reports (October 1986) nutrient information contains 2 positive (fiber and protein) and 3 negative (sugar, sodium, and fat) nutrients.

Russo, et.al (1986) argue that summary measures should not contain negative nutrient information because there is no standard (e.g., R.D.A.) level for negative nutrients across any mix of consumers. This does not, however, reduce the meaningfulness of the Consumer Reports summary data which depends in part on negative nutrient cues. What is of concern is the relative weight given to each nutrient, negative or positive In terms of persuasive effects, perceptions of relative brand nutritional levels may have greater influence on purchase decisions than brand levels relative to an externally imposed standard.

Examination of dry cereal boxes revealed display of 2 sections of nutrition information. One contained the most of five nutrients cited here, while the other included the remainder of the five plus vitamins and minerals. Consumer Reports acknowledges that individuals may want to consider vitamins and minerals, but that they're not included in their summary measure because most dry "cereals" are fortified with vitamins and most people get sufficient daily vitamins in the other foods they consume every day. Except for a few cereal brands which actively promote 100% U.S. RDA vitamin and mineral content (e.g., Total, Product 19) most contain between one-fourth and one-third of the required daily U.S. RDA levels. The purpose of this research is not to argue the issue of which nutrient information should be displayed in a publication, but rather to -compare individual use of nutrient cues which are published with that of an external, "expert" source. The question involves the efficiency of information markets based on availability of an influential complete format of nutritional quality of brands and acceptability of overall summary ratings by consumers.

Conceivably a person who examines a "complete" format display of brand ratings could learn the algorithm used by the information provider (e.g., Consumer Reports). This study does not propose to test the learning effect, but rather is concerned with the ability of consumers to achieve comparable brand ratings by using their own self-styled method of evaluation. This achievement can then be decomposed to provide an evaluation of the tendency of individuals to match the algorithmic formulation of external sources of summary rating scales. The following section describes the lens model methodology employed to test the variation in use of a matrix format of nutrient information across subjects.

Technique of Analysis: Lens Model

Brunswik's Lens Model technique (Brunswik, 1955; Hursch, Hammond, and Hursch, 1964; Castellan, 1972, 1973) was employed to analyze the data. This technique has been infrequently applied to marketing problems (Davis and Plas, 1983; Holbrook, 1981; Woodside and Taylor, 1986). Objective measures of ecological variables are often difficult to obtain in marketing studies. Tapp (1984) contends that a measure of post-purchase satisfaction cannot be obtained objectively to validate consumer inference in a probabilistically functional context when satisfaction is basically a subjective response. However, indirect indicators of satisfaction can be obtained through objective measures.

In the case of dry breakfast cereals, it is doubtful that anyone would personally analyze the nutritional content. An image of a brand derived from objective product information and/or promotional campaigns may be all most people need to achieve an acceptable level of brand satisfaction, taste and other factors not withstanding. In the context of this study, Consumer Reports use of nutrient levels to construct the CR summary measure of nutritional value by brand provides the needed objectively measurable ecological variable.

The Consumer Reports (CR) measure is obtained by their expert (but subjective) weighting of objective nutritional content measures. The subjectivity is observable in the regression coefficients of the objective nutritional variables (e.g., protein content) on the ecological side of the model. By publishing summary nutrition values for each cereal, CR is creating an ecological standard by which many consumers will evaluate cereal in purchase decisions. A public policy issue is raised with regard to the claim that their summary measure is valid for a majority of consumers who base their purchase decisions upon it. It thus becomes an objective criterion for many consumers, but not necessarily ecologically valid. Our use of the lens model is testing the ecological validity of the CR summary measure for the average consumer. This, of course, assumes the average consumer has sufficient knowledge of the nutritional components presented here to validly form his/her personal summary criterion measure. An extension would involve replicating this study on a group of "nutritional experts". In this sense then, achievement is a misnomer somewhat in that it is used more to evaluate the ecological validity than to measure the learning sense of achievement.

The formulation of this study in the Lens Model context is diagrammed below in Figure 1. In this formulation, the BE are estimated using OLS with the nutrient cues acting as the independent variables and YE, Consumer Reports nutritional value, as the dependent variable. Similarly, the Bs's are estimated with OLS with Ys as the dependent variable. Thus, a distinct set of Bs's as well as scores for achievement (ra) and matching (rm) will be estimated for each subject Achievement scores provide a measure of the efficiency of the matrix format of nutrient cues in the marketing of brand by brand information. Matching is simply a measure of each subjects ability or tendency to conform to the linear use of cues by a sole expert source.

Each subject views the nutrient cues stochastically, with the distribution of ENs representing the within subject variation. Each subject's ability to utilize the nutrient cues in the same way as Consumer Reports can be measured by rm, the level of matching. rm is the simple correlation between YE and Ys and is a measure of the correspondence between respective B-weights for each cue (Castellan, 1973). The achievement of each subject in estimating the "true" nutritional value of each brand (YE's) is the simple correlation, ra, between YE and Ys for the 40 brands. (Castellan, 1973).

Because the estimates of the parameters assumes linearity, the correlation of the residual variances can be used to estimate the proportion of non- linearity or configurality which each subject is able to discern from the ecological non-linear usage of cues. The level of achievement, ra, can be decomposed into linear and nonlinear components in the following manner (Castellan, 1973):


The first term rmRERs represents the portion of achievement which derives from linear matching. The second term EQUATION represents the portion of the achievement score which derives from non-linear (or configural) matching.





Students in a graduate business program at a large Eastern University voluntarily participated as subjects in the experiment. Half the students were from foreign countries, most of whom were relatively unfamiliar with cereal brand names. The other half were American students who were familiar with many brand names. Nationality should therefore be able to be used to manipulate brand name familiarity. Because cereal brand names may influence a person's perception of the nutritional value of that brand, a stronger manipulation can be achieved. One half of the subjects were randomly assigned to a brand-name-available condition while the other half received no brand-name cue in their instrument, regardless of nationality. Domestic subjects in the brand name available condition should be most affected in nutrition appraisal.

Students were selected from an MBA class to increase the likelihood of higher motivation than undergraduates. In addition, partial course credit was given for performance of this task. Two products were used of which cereals were one. Students took between 20 and 45 minutes to complete the task, depending upon which conditions they were assigned. Because there were 40 brands with five nutrients each, it is highly likely that no subject used all 5 nutrient cues. Because the purpose of the study is to evaluate the ecological validity of highly influential published product information, it is hoped that subjects will only use those nutrients which are critical to their nutritional well being in evaluating the various brands. Students performing this task expressed a desire to be able to program this information to make brand by brand nutritional evaluation.


The matrix format excluding the Consumer Reports (CR) summary measure was used to provide nutritional information by brand. The names of the five nutritional components with the units for each (e.g. grams of sugar per one ounce serving) were listed at the top of the vectors of nutrient cue values for each brand. The five nutrients were fiber, protein, sugar, sodium, and fat. Fiber and protein were considered to be positive nutrients while sugar, sodium, and fat are negative nutrients (c.f. Russo, et al., 1986). Therefore, increasing amounts of protein and fiber should result in higher nutritional values; increasing amounts of sodium, sugar, and fat, on the other hand, should lead to lower nutritional values.

The cover sheet of the survey instrument contained the professional reference manipulation. As with brand names, this was a between subjects condition. Subjects were placed randomly in one of three groups: (1) No professional reference made; (2) A sentence stating that the nutrient/attribute ratings were from an "independent professional" organization; or, (3) the same sentence as in (2) but with "Consumer Reports" substituted for "independent professional" organization.


In the column to the right of the nutrient scores for the 40 brands of cereal used, subjects were instructed to write a value from 000 to 100 to indicate their perception of the overall nutritional value of each brand, where 000 represented the lowest possible nutritional value and 100 the highest possible nutritional value. The same nutritional scale was used by Consumer Reports to report the CR summary measure of dry cereal nutritional value to readers for each brand.

After completing this task, subjects were instructed to rate the importance of each of the five nutrients in evaluating the nutritional value of each brand. This rating was done on a seven-point scale anchored by not-at-all important (=1) to very important (=7). Finally subjects were instructed to complete items which indicated their prior behavioral response (purchase, use) to various brands of cereal, as well as selected demographic classification items.


A separate lens model analysis was run for each subject. Patterns of cue utilization varied considerably. No subjects weighed cues in exactly the same mathematical pattern as Consumer Reports, though a few were close. Most subjects tended to use one or two cues while virtually ignoring others. A probability = .05 was required for the coefficients of cues to be statistically different from zero. Any coefficient with a probability(t) > .05 was converted to zero for use in cluster analysis..

The benchmark for ecological matching, is given by the following relationship:

YE=62.3+1.63(FIBER)+2.15(PROTEIN)-0.06(SODIUM-1.69(FAT)-2.28(SUGAR)      (2)

(p<) (.0001)  (.0001)                 (.0001)            (.0001)              (.0001)          (.0001)

Equation (2) represents the relationship between the summary measures provided by Consumer Reports and the five nutrient cues on which the summary ratings were based.

To assess the patterns of cue use among subjects and render the results more understandable, a cluster analysis was run. The clusters can be considered to be benefit segments. Subjects tended to significantly use only two or three of the five cues in making evaluations. Subjects who exhibited the highest level of achievement tended to cluster in a group which used fiber, sugar, and sodium to evaluate the brands. All high achievers utilized a combination which included at least one positive and one negative nutrient. High achievers also tended to be high on linear matching. This may have resulted in the relatively low level of configural cue usage by Consumer Reports Nearly all achievement, high or low, resulted from matching linear rather than nonlinear ecological cue usage by subjects. High achievers tended to be American students who were not overly concerned with any one nutrient, but rather attempted to objectively evaluate brands- using data at hand.



Table 1 shows the results of the Cluster Analysis. Observation 34 contains the nutrient cue coefficients obtained by regressing the CR summary rating on the values of the nutrient cues across the 40 brands of cereal. This represents the ecological (left) side of the lens model in Figure l. Each of the remaining observations represent the coefficients obtained by regressing each subject's summary evaluation on the nutrient cues across the 40 brands of cereals.

The analysis indicates that non-subjects used all cues with precisely the same weighting structure as CR. In fact, most subjects used only a subset of cues, yet many attained high achievement scores. One reason for this may be a high level of cue intercorrelation, i.e., redundancy in relative ranking of pairs of cues across brands. Table 2 below shows the correlation matrix for the five nutrient cues used in this experiment. This matrix shows that redundancy occurs between fiber and sodium, protein and sodium and fat and sugar. All three pairs are negatively correlated (pc.05). These negative correlations indicate that, to some degree, a person could use one of each pair of cues and still attain a reasonable level of achievement (ra).

The seven resulting clusters represent similar patterns of cue usage by subjects within each cluster. Cluster l subjects show no pronounced use of any set of cues. Observations 11 through 15 are foreign students who used negative nutrients in an algebraically inverse way than Consumer Reports. Cluster 2 and 7 subjects placed a heavy emphasis on protein. The Cluster 2 subject was a foreign student who used the fat cue inversely. Cluster 3 subjects primarily emphasized fat content. Cluster 4 subjects heavily emphasized fiber and sugar content. Cluster 5 subjects emphasized fat and sodium content. Cluster 6 subjects emphasized a combination of fiber, sugar, and fat.

Subjects who exhibited the highest levels of nonlinear cue matching tended to use only negative nutrients linearly. Negative nutrient cue usage has been found to be more important in brand evaluations and purchase decisions (Russo, et.al., 1986). However, in this study, achievement was usually lowered by failure to consider positive nutrients in a linear function.

Subjects who exhibited the lowest levels of achievement evaluated at least one negative nutrient inversely. They tended to be foreign students who perceived fat, sugar, and sodium as being positively related to nutritional value. They came from countries as diverse in culture as India, Germany, and Taiwan and were among the best and more conscientious students. Likelihood of arbitrary responses was therefore extremely low.


Results presented above provide an approach to analyzing consumer response to the availability of nutrient cues in a matrix information format . Utilizing the probabilistic functional approach to cue evaluation, the lens model technique was applied in an information market context to nutrient cue processing by potential cereal consumers. The focus was on the micro issue of variation in consumer use of nutrient cues. Results indicate that assumptions of homogeneity of cue utilization in cross sectional studies is of questionable validity. Failure to observe aggregate cue usage effects in cross sectional studies may occur when effects exist at a more disaggregate level.



Cluster analysis revealed patterns of cue usage which may be construed as nutritional benefit segments the market for dry cereals. Even within the clusters, variation in cue coefficients existed. This variation supports the probabilistic functional theory of cue use by individuals (Brunswik, 1955).

The importance of positive nutrient cues in attaining high achievement scores raises doubts about the contention by Russo, et al. (1986) that positive nutrients do not affect purchase decisions. In the Russo, et al study, positive nutrients values for fiber and protein were not available to subjects in the display boards. Only the positive nutrients values for vitamins and mineral, which Consumer Reports contends do not significantly discriminate among brands, were available. Russo, et al. results support this Consumer Reports contention. Though we did not measure purchase response, results indicate that evaluation of overall nutritional quality of brand is as sensitive to positive as to negative nutrient cues.

Increasing use of brand matrix and summary formatted information is being made possible through electronic as well as print media. The development of high-powered personal computers, communication devices, and artificial intelligence software make it possible for consumers to design their own algorithm to compute summary nutritional values from either self-collected (e.g. from cereal boxes) or pre-collected (e.g. Consumer Reports) data sources. Individuals can potentially generate their own matrices and summaries of brand-nutrient information to be built into an overall nutrient/conditioning program.

Additional studies are needed which examine both other product classes as well as other more complex configurations of potential cue usage. This research provides one potential application of the lens model in the marketing literature to the problems inherent in information markets. Difficulties inherent in finding objective measures of subjective consumer responses such as satisfaction (Tapp, 1984) can be remedied more readily in information markets. Rapid increases in the number of published summary measures of brand attributes provide a rich array of application possibilities.


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